Math 209

Statistics 209

Q1. Use the classical definition to find the probability of the following event: Rolling a fair die once and getting a number less than 2. Express your answer as a decimal rounded to one decimal place.

Q2. Use the classical definition to find the probability of the following event: Flipping a fair coin twice and getting 2 heads. Express your answer as a decimal rounded to 1 decimal place.

Q3. Use the addition rule to find the probability of the following event: Obtaining a sum of 6 or doubles (same number on each die) when a pair of dice is rolled once. Express your answer as a decimal rounded to 1 decimal place.

Q4. A state lottery involves the random selection of five numbers between 1 and 69 inclusive. If you select one five number combination, what is the

**probability** that it will be the winning combination? Assume the order in which the numbers are drawn does not matter and repeats are not allowed.

A. 11,238, 513

B. 1/11,238,513

C. 1/1,000,000

D. None of these

Q5. Suppose that A and B are independent events with P(A) = 0.8 and P(B) = 0.5. Use this information to answer questions 5 through 8.

Find P (A and B). Express your answer as a decimal.

Q6. Find P (A or B). Express your answer as a decimal.

Q7. Find P(A|B). Express your answer as a decimal.

Q8. Choose whether the following statement is true or false: A and B are mutually exclusive events.

a) True

b) False

Q9. The next three questions involves Bayes’s theorem. Use the following information to answer questions 9, 10, and 11.

In the billing department of a local city, Nancy, Bob, and Mary prepare and mail out 50%, 30%, and 20% of the real-estate tax bills, respectively, to property owners. The bills are verified by the treasurer before mailing. If 0.5% of the tax bills prepared by Nancy, 0.3% of the tax bills prepared by Bob, and 1.0% of the tax bills prepared by Mary are inaccurate, what are the probabilities that an inaccurate statement detected by the treasurer at final verification was prepared by:

a) Nancy

Express your answer as decimal rounded to 1 decimal place

Q10. b) Bob

Express your answer as a decimal rounded to 1 decimal place.

Q11. c) Mary

Express your answer as a decimal rounded to 1 decimal place.

Q12. Choose whether the following statement is true or false:

The function F (X) =5-X/ 10 FOR X= 1, 2, 3, 4 can serve as a discrete probability distribution.

a) True

b) False

Q13. Compute the mean of the function in question 12.

Q14. Compute the standard deviation of the function in question 12.

Q15. Use the binomial distribution to find the probability that five rolls of a fair die will show exactly two threes. Express your answer as a decimal rounded to 1 decimal place.

Q16. At the terminal of a certain airline, records disclose that 10% of their flights arrive early, 70% arrive on time, 12% arrive somewhat late, and 8% arrive very late. Use the formula for the multinomial distribution to determine the probability that in six randomly selected flights, one will arrive early, three will arrive on time, two will be somewhat late, and none will be very late. Express your answer as a decimal rounded to 2 decimal places.

Q17. Among 15 applicants for sales positions in a corporation, 8 have college degrees and 7 do not have college degrees. If 4 are randomly selected for interviews, use the hypergeometric distribution to find the probability that all have college degrees. Express your answer as a decimal rounded to 2 decimal places.